Multilinear interpolation between adjoint operators

Loukas Grafakos; Terence Tao

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Multilinear interpolation between adjoint operators

Loukas Grafakos·Terence Tao

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Abstract

Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak $L^q$ estimate for a single index $q$ (which may be less than one) and that all the adjoints of the multilinear operator are of similar nature, and thus they also satisfy the same weak $L^q$ estimate. Under this assumption, in this expository note we give a general multilinear interpolation theorem which allows one to obtain strong type boundedness for the operator (and all of its adjoints) for a large set of exponents. The key point in the applications we discuss is that the interpolation theorem can handle the case $q \leq 1$. When $q > 1$, weak $L^q$ has a predual, and such strong type boundedness can be easily obtained by duality and multilinear interpolation.

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BibTeX RIS

Loukas Grafakos, Terence Tao. 2001-11-12. Multilinear interpolation between adjoint operators. https://arxiv.org/abs/math/0111141

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